In this work we are concerned with an efficient numerical solution of a perfectly matched layer (PML) system for a Maxwell scattering problem. The PML system is discretized by the edge finite element method, resulting in a symmetric but indefinite complex algebraic system. When the real and imaginary parts are considered independently, the complex algebraic system can be further transformed into a real generalized saddle-point system with some special structure. Based on an crucial observation to its Schur complement, we construct a symmetric and positive definite block diagonal preconditioner for the saddle-point system. Numerical experiments are presented to demonstrate the effectiveness and robustness of the new preconditioner.
DOI : 10.1051/m2an/2014058
Mots-clés : Maxwell scattering problem, edge finite elements, PML equations, Schur complement-type preconditioner
@article{M2AN_2015__49_3_839_0,
author = {Hu, Qiya and Liu, Chunmei and Shu, Shi and Zou, Jun},
title = {An effective preconditioner for a {PML} system for electromagnetic scattering problem},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {839--854},
publisher = {EDP-Sciences},
volume = {49},
number = {3},
year = {2015},
doi = {10.1051/m2an/2014058},
mrnumber = {3342230},
zbl = {1318.35115},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014058/}
}
TY - JOUR AU - Hu, Qiya AU - Liu, Chunmei AU - Shu, Shi AU - Zou, Jun TI - An effective preconditioner for a PML system for electromagnetic scattering problem JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 839 EP - 854 VL - 49 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014058/ DO - 10.1051/m2an/2014058 LA - en ID - M2AN_2015__49_3_839_0 ER -
%0 Journal Article %A Hu, Qiya %A Liu, Chunmei %A Shu, Shi %A Zou, Jun %T An effective preconditioner for a PML system for electromagnetic scattering problem %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 839-854 %V 49 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014058/ %R 10.1051/m2an/2014058 %G en %F M2AN_2015__49_3_839_0
Hu, Qiya; Liu, Chunmei; Shu, Shi; Zou, Jun. An effective preconditioner for a PML system for electromagnetic scattering problem. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 3, pp. 839-854. doi : 10.1051/m2an/2014058. http://www.numdam.org/articles/10.1051/m2an/2014058/
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